OFFSET
0,3
COMMENTS
Compare definition of g.f. to:
(1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x).
(2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 (A000108).
(3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 (A001764).
(4) E(x) = 1 + x/E(-x*E(x)^7)^4 when E(x) = 1 + x*E(x)^4 (A002293).
(5) F(x) = 1 + x/F(-x*F(x)^9)^5 when F(x) = 1 + x*F(x)^5 (A002294).
The first negative term is a(68). - Georg Fischer, Feb 16 2019
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 24*x^3 + 181*x^4 + 1893*x^5 + 20601*x^6 +...
Related expansions:
A(x)^9 = 1 + 9*x + 63*x^2 + 516*x^3 + 4563*x^4 + 45207*x^5 + 486579*x^6 +...
A(-x*A(x)^9)^3 = 1 - 3*x - 15*x^2 - 64*x^3 - 798*x^4 - 8277*x^5 - 99411*x^6 -...
MATHEMATICA
m = 21; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^9]^3 + O[x]^m, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 06 2019 *)
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x/subst(A^3, x, -x*subst(A^9, x, x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jun 05 2012
STATUS
approved